Abstract
Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in two-player zero-sum games, but no guarantees in non-zero-sum games or in games with more than two players. We describe an agent that is able to defeat a variety of realistic opponents using an exact Nash equilibrium strategy in a three-player imperfect-information game. This shows that, despite a lack of theoretical guarantees, agents based on Nash equilibrium strategies can be successful in multiplayer games after all.
Highlights
Nash equilibrium has emerged as the central solution concept in game theory, in large part due to the pioneering PhD thesis of John Nash proving that one always exists in finite games [1]
For two-player zero-sum games, Nash equilibrium enjoys this “unbeatability” property. This has made it quite a compelling solution concept, and agents based on approximating Nash equilibrium have been very successful and have even been able to defeat the strongest humans in the world in the popular large-scale game of two-player no-limit Texas hold ’em poker [3,4]
Nash equilibrium strategy is able to outperform all of the agents from the class. This suggests that agents based on using Nash equilibrium strategies can be successful in multiplayer games, despite the fact that they do not have a worst-case theoretical guarantee
Summary
Nash equilibrium has emerged as the central solution concept in game theory, in large part due to the pioneering PhD thesis of John Nash proving that one always exists in finite games [1]. For two-player zero-sum games, Nash equilibrium enjoys this “unbeatability” property This has made it quite a compelling solution concept, and agents based on approximating Nash equilibrium have been very successful and have even been able to defeat the strongest humans in the world in the popular large-scale game of two-player no-limit Texas hold ’em poker [3,4]. The strongest existing agents for large multiplayer games have been based on approaches that attempt to approximate Nash equilibrium strategies [16,17] They apply the counterfactual regret minimization algorithm [18], which has been used for two-player zero-sum games and has resulted in super-human level play for both limit Texas hold ’em [19] and no-limit Texas hold. Since we just experimented on one specific game there is no guarantee that this conclusion would apply beyond this to other games, and more extensive experiments are needed to determine whether this conclusion would generalize
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